Abstract : Roughness of the boundaries presents a severe limitation for the performance of multilayer x-ray mirrors with small periods A < 50 A, and makes ir difficult to produce efficient multilayers with periods approaching the size of the atoms in the coating. Reflectivities are reduced by a large factor from the theoretical smooth boundary value, for example nearly a factor 10 for a coating with period A = 30 A. If all the loss in reflectivity would appear as scattered light within the field of view of an instrument, one would not be able to obtain high contrast images of extended objects; each image element would be surrounded by a halo of scattered light of much higher total intensity.